Introduction

Real GDP: To determine “real” GDP, its nominal value must be adjusted to take into account price changes to allow us to see whether the value of output has gone up because more is being produced or simply because prices have increased. Moreover, my data set from IMF is Annual percent change, which makes it easier for me later. Inflation Data is also annual percent change.

#Real GDP

real_GDP_raw<- read_excel("SK_n_ARG_realGDP.xls")

#I'm just reusing cleaned excel data from prosposal.
realGDP_data<- real_GDP_raw%>%
  rename(Year = 1)%>%
  select(1,2)

#Since it is an annual data, i have to past "01-01" at the end of every year to make it a time-series data.
realGDP_data$Year <- as.Date(paste0(realGDP_data$Year, "-01-01"))
realGDP_data <- realGDP_data %>% filter(Year > as.Date("1991-01-01"))

#Inflation Data
inflation_raw<- read_excel("inflation_data.xlsx")

inflation_data<- inflation_raw%>%
  rename(Year = 1)%>%
  mutate(Argentina = Argentina *100)%>%
  select(1,2)

inflation_data$Year <- as.Date(paste0(inflation_data$Year, "-01-01"))

ggplot(data = inflation_data) +
  geom_line(aes(x = Year, y = Argentina, color = "Argentina")) +
  labs(title = "Inflation of Argentina",
       x = "Year",
       y = "Inflation Rate",
       color = "Country") +
  scale_color_manual(values = c("Argentina" = "blue", "South Korea" = "red")) 

inflation_data <- inflation_data %>% filter(Year > as.Date("1991-01-01"))

Inflation is too high around the late 1980s and, and moreover, inflation flunctuate too much in Argentina, so I decided to go with realGDP data for my final Project for a predicting variable. Here’re are inflation and real GDP graph for Argentina after 1991.

ggplot(data = realGDP_data) +
  geom_line(aes(x = Year, y = Argentina, color = "Argentina")) +
  labs(title = "Real GDP of Argentina",
       x = "Year",
       y = "Inflation Rate",
       color = "Country") +
  scale_color_manual(values = c("Argentina" = "blue"))

ggplot(data = inflation_data) +
  geom_line(aes(x = Year, y = Argentina, color = "Argentina")) +
  labs(title = "Inflation of Argentina",
       x = "Year",
       y = "Inflation Rate",
       color = "Country") +
  scale_color_manual(values = c("Argentina" = "blue", "South Korea" = "red"))

South Korea Data from 1993 to 2013 Argentina Data from 2004 to 2023 This is where the original idea came from (kind of).

History Lesson: According to a NY times article, the inflation has gone up to 90% this year and this is not looking good for the country, From this week election, it elected a very right-wing politician with promises on freedom of the market and changing of the currency from Argentinian pesos to US dollars and such.

South Korea after Asian Financial Crisis in 199: What similar about this situation is that they got a lot of financial bailouts from financial institutions around the world, more prominently the IMF (International Monetary Fund), and had a very corporate-centered economic restructuring for regulations and laws. Similarly, Argentina has the most bailout loan from IMF currently and a new economic restructuring with the new political party.

SK_fake_data<- real_GDP_raw%>%
    rename(Year = 1, `South Korea` = 3)
SK_fake_data$Year <- as.Date(paste0(SK_fake_data$Year, "-01-01"))
SK_fake_data<- SK_fake_data %>%
    select(Year,3)%>%
  filter(Year > "1993-01-01" & Year < "2013-01-01")%>%
  mutate(Year = row_number())
ARG_fake_data<- realGDP_data%>%
  select(Year,2)%>%
  filter(Year > "2004-01-01")%>%
  mutate(Year = row_number())

fake_data<- left_join(SK_fake_data,ARG_fake_data)
## Joining, by = "Year"
ggplot(data = fake_data) +
  geom_line(aes(x = Year, y = Argentina, color = "Argentina")) +
  geom_line(aes(x = Year, y = `South Korea`, color = "South Korea")) +
  labs(title = "realGDP Comparison",
       x = "Year",
       y = "Inflation Annual Rate",
       color = "Country") +
  scale_color_manual(values = c("Argentina" = "blue", "South Korea" = "red"))

Argentina is one of the world’s major exporters of soybeans and meat. Soybean and cattle data are from ‘Food and Agricultural Organization of the United Nations’.

soybean_prod_arg <- read.csv("Soybean_Prod_ARG.csv")%>%
  select(Year, Value)

#NA variable to be used for calculation for annual change
soybean_prod_arg$Percentage_Change <- NA

# Calculate annual percentage change using a 'for' loop
for (i in 2:nrow(soybean_prod_arg)) {
  soybean_prod_arg$Percentage_Change[i] <- ((soybean_prod_arg$Value[i] - soybean_prod_arg$Value[i - 1]) / soybean_prod_arg$Value[i - 1]) * 100
}

soybean_prod_arg$Year <- as.Date(paste0(soybean_prod_arg$Year, "-01-01"))

soybean_prod_arg<- soybean_prod_arg%>%
  filter(Year> "1991-01-01")

#This data is to not mess with original data and for visualization
GDP_fake<- realGDP_data%>%
  filter(Year < "2022-01-01")

ggplot(data = soybean_prod_arg) +
  geom_line(aes(x = Year, y = Percentage_Change, color = "Soybean Production")) +
  geom_line(aes(x = Year, y = GDP_fake$Argentina, color = "Argentina real GDP")) +
  labs(title = "Soybean Production vs Argentina Real GDP",
       x = "Year",
       y = "Soybean Production Annual Percentage Change",
       color = "Country") +
  scale_color_manual(values = c("Soybean Production" = "blue", "Argentina real GDP" = "red"))

Fun Fact: Argentinians are among the world’s largest producer and consumer of cattle/beef.

ARG_Cattle_data_raw<- read.csv("ARG_Cattle_data.csv")

ARG_Cattle_data <- ARG_Cattle_data_raw%>%
  select(Year, Value)%>%
  rename(Cattle_count = 2)
ARG_Cattle_data$Year <- as.Date(paste0(ARG_Cattle_data$Year, "-01-01"))

#NA variable to be used for calculation for annual change
ARG_Cattle_data$Percentage_Change_Cattle <- NA
# Calculate annual percentage change using a 'for' loop
for (i in 2:nrow(ARG_Cattle_data)) {
  ARG_Cattle_data$Percentage_Change_Cattle[i] <- ((ARG_Cattle_data$Cattle_count[i] - ARG_Cattle_data$Cattle_count[i - 1]) / ARG_Cattle_data$Cattle_count[i - 1]) * 100
}
ARG_Cattle_data<- ARG_Cattle_data %>%
  filter( Year > "1991-01-01" & Year < "2022-01-01")

ggplot(data = ARG_Cattle_data) +
  geom_line(aes(x = Year, y = Percentage_Change_Cattle, color = "Cattle Production Annual Percentage Change"))+
      geom_line(aes(x = Year, y = GDP_fake$Argentina, color = "Argentina real GDP")) +
  labs(title = "Cattle Production vs Argentina Real GDP",
       x = "Year",
       y = "Cattle Production Annual Percentage Change",
       color = "Country") +
  scale_color_manual(values = c("Cattle Production Annual Percentage Change" = " blue", "Argentina real GDP" = "red"))

Gross Debt: By comparing what a country owes with what it produces, the debt-to-GDP ratio reliably indicates that particular country’s ability to pay back its debts. Gross Debt data is from IMF.

However, Gross Debt Annual Percentage Change is in opposite trend of real GDP as it is calculated from GDP. Therefore, I created Negative Gross Debt Annual Percentage Change by muliplying every data point with ‘-1’ in the loop.

#Original Gross Debt Data Cleaning
ARG_gross_debt_raw<- read.csv("ARG_gross_debt.csv")
#Percentage of GDP
ARG_gross_debt<- ARG_gross_debt_raw%>%
  mutate(Year = as.Date(DATE))%>%
  select(3,2)%>%
  rename(Gross_debt =2)%>%
  filter(Year< "2022-01-01")

#Gross Debt of Argentina for 1991
ARG_gross_debt$Gross_debt_Per_Change <- NA

# Calculate percentage change using a for loop
for (i in 2:nrow(ARG_gross_debt)) {
  ARG_gross_debt$Gross_debt_Per_Change[i] <- ((ARG_gross_debt$Gross_debt[i] - ARG_gross_debt$Gross_debt[i - 1]) / ARG_gross_debt$Gross_debt[i - 1]) *100
}
ARG_gross_debt$Gross_debt_Per_Change[1] = ARG_gross_debt$Gross_debt_Per_Change[2]


ggplot(data = ARG_gross_debt) +
  geom_line(aes(x = Year, y = Gross_debt_Per_Change, color = "Gross Debt Annual Percentage Change"))+
    geom_line(aes(x = Year, y = GDP_fake$Argentina, color = "Argentina real GDP")) +
  labs(title = "Gross Debt Annual Percentage Change",
       x = "Year",
       y = "Gross Debt Annual Percentage Change",
       color = "Country") +
  scale_color_manual(values = c("Gross Debt Annual Percentage Change" = "blue", "Argentina real GDP" = "red"))

ARG_gross_debt_negative<- ARG_gross_debt_raw%>%
  mutate(Year = as.Date(DATE))%>%
  select(3,2)%>%
  rename(Gross_debt =2)%>%
  filter(Year< "2022-01-01")
#Negative gross Data for 1991
ARG_gross_debt_negative$Gross_debt_Per_Change <- NA

# Calculate percentage change using a for loop
for (i in 2:nrow(ARG_gross_debt_negative)) {
  ARG_gross_debt_negative$Gross_debt_Per_Change_negative[i] <- -1*( (ARG_gross_debt_negative$Gross_debt[i] - ARG_gross_debt_negative$Gross_debt[i - 1]) / ARG_gross_debt_negative$Gross_debt[i - 1]) *100
}
ARG_gross_debt_negative$Gross_debt_Per_Change_negative[1] = ARG_gross_debt_negative$Gross_debt_Per_Change_negative[2]   


ggplot(data = ARG_gross_debt_negative) +
  geom_line(aes(x = Year, y = Gross_debt_Per_Change_negative, color = "Negative Gross Debt Annual Percentage Change"))+
    geom_line(aes(x = Year, y = GDP_fake$Argentina, color = "Argentina real GDP")) +
  labs(title = "Negative Gross Debt Annual Percentage Change",
       x = "Year",
       y = "Negative Gross Debt Annual Percentage Change",
       color = "Country") +
  scale_color_manual(values = c("Negative Gross Debt Annual Percentage Change" = "blue", "Argentina real GDP" = "red"))

Brazil is Argentina’s Neighbor and one of its most important trade partner being two of the biggest countries in South America. Although Brazil’s economy is not the best, it doesn’t fluctuate as much as Argentina’s. I use Brazil’s realGDP data from IMF.

brazil_realGDP_raw<-read_excel("Brazil_realGDP.xls")

brazil_realGDP_data<- brazil_realGDP_raw%>%
  rename(Year = 1)

brazil_realGDP_data$Year <- as.Date(paste0(brazil_realGDP_data$Year, "-01-01")
                                    )
brazil_realGDP_data <- brazil_realGDP_data %>% filter(Year > as.Date("1991-01-01") & Year < as.Date("2022-01-01"))

ggplot(data = brazil_realGDP_data) +
  geom_line(aes(x = Year, y = RealGDP, color = "Brazil real GDP"))+
    geom_line(aes(x = Year, y = GDP_fake$Argentina, color = "Argentina real GDP")) +
  labs(title = "Argentina v. Brazil realGDP",
       x = "Year",
       y = "Brazil real GDP",
       color = "Country") +
  scale_color_manual(values = c("Brazil real GDP" = "blue", "Argentina real GDP" = "red"))

All variables used in this project is plotted against each other here:

#cleaned Data
realGDP_data<- realGDP_data%>% slice(1:30)
head(realGDP_data)
## # A tibble: 6 × 2
##   Year       Argentina
##   <date>         <dbl>
## 1 1992-01-01      10.3
## 2 1993-01-01       6.3
## 3 1994-01-01       5.8
## 4 1995-01-01      -2.8
## 5 1996-01-01       5.5
## 6 1997-01-01       8.1
#Not to mess with the cleaned data of Argentina's real GDP data, I created a final data with variables used for this projects.
#I removed the Year format, as I cannot used it as tsibble because there are missing data when months and dates are involved.
final_table <- realGDP_data %>%
  mutate(
    Year = as.double(Year),  # Convert Year to Date format
    Cattle = ARG_Cattle_data$Percentage_Change_Cattle,
    Soybean = soybean_prod_arg$Percentage_Change,
    Gross_Debt = ARG_gross_debt$Gross_debt_Per_Change,
    Brazil_realGDP = brazil_realGDP_data$RealGDP,
    Gross_debt_negative = ARG_gross_debt_negative$Gross_debt_Per_Change_negative
  )
#Format of the Date changed as it was changed to double.
#This makes it 1993 to 2022
final_table <- final_table %>%
  mutate(Year = 1993 + row_number() - 1) %>%
as_tsibble(index = Year)

final_table
## # A tsibble: 30 x 7 [1Y]
##     Year Argentina  Cattle Soybean Gross_Debt Brazil_realGDP Gross_debt_negative
##    <dbl>     <dbl>   <dbl>   <dbl>      <dbl>          <dbl>               <dbl>
##  1  1993      10.3 -4.59     4.12        7.74           -0.5               -7.74
##  2  1994       6.3  0.862   -2.34        7.74            4.7               -7.74
##  3  1995       5.8 -0.890    6.11        5.70            5.3               -5.70
##  4  1996      -2.8 -3.41     3.52        8.17            4.4               -8.17
##  5  1997       5.5  0.223    2.60        5.86            2.2               -5.86
##  6  1998       8.1  0.668  -11.6        -2.69            3.4                2.69
##  7  1999       3.9 -8.95    70.2         7.80            0.3               -7.80
##  8  2000      -3.4 10.1      6.77       14.0             0.5              -14.0 
##  9  2001      -0.8 -0.0656   0.679       4.92            4.4               -4.92
## 10  2002      -4.4 -9.46    33.5        17.6             1.4              -17.6 
## # … with 20 more rows
# Plotting using ggplot
ggplot(data = final_table) +
  geom_line(aes(x = Year, y = Argentina, color = "Argentina real GDP")) +
  geom_line(aes(x = Year, y = Cattle, color = "Cattle")) +
  geom_line(aes(x = Year, y = Soybean, color = "Soybean")) +
  geom_line(aes(x = Year, y = Gross_Debt, color = "Gross Debt")) +
  geom_line(aes(x = Year, y = Brazil_realGDP, color = "Brazil Real GDP")) +
  labs(
    title = "Prediction Variables",
    x = "Year",
    y = "Annual Percentage Changes",
    color = "Variables"
  )

AutoRegression on ARG_ RealGDP

The data looks stationary because all my values are percentge change from their previous years. Due to the unitroot_kpss test statistic of 0.1740834 , it confirms that the data is stationary and unitroot_ndiffs says that I don’t need any differencing for Argentina real GDP data. The ACF graph shows that the data is white noise and this is stationary.

#Check if Argentina Real GDP needs Differencing
final_ARG_RealGDP = final_table|> select(Argentina)
#test-statistic
final_ARG_RealGDP|> features(Argentina, unitroot_kpss)
## # A tibble: 1 × 2
##   kpss_stat kpss_pvalue
##       <dbl>       <dbl>
## 1     0.174         0.1
#if needs differencing, how much?
final_ARG_RealGDP|>features(Argentina, unitroot_ndiffs)
## # A tibble: 1 × 1
##   ndiffs
##    <int>
## 1      0
summary(ur.kpss(final_ARG_RealGDP$Argentina)) 
## 
## ####################### 
## # KPSS Unit Root Test # 
## ####################### 
## 
## Test is of type: mu with 2 lags. 
## 
## Value of test-statistic is: 0.1741 
## 
## Critical value for a significance level of: 
##                 10pct  5pct 2.5pct  1pct
## critical values 0.347 0.463  0.574 0.739
#ACF    
final_ARG_RealGDP|>ACF() |> autoplot()                 
## Response variable not specified, automatically selected `var = Argentina`

ARIMA models

R’s in-house ARIMA model. With this, I tested the ARIMA model, which gave me ARIMA model of (0,0,0) whose forecast on the long-term is 0. Ljung_box test confirms it is white noise. This fit_AR of Argentina’s real GDP gave an AIC of 159.51.

#normal ARIMA
fit_AR1<- final_table|>
  model (ARIMA(Argentina))

fc_AR1 = fit_AR1 |>
  forecast(h = 5)
fc_AR1 |> autoplot() + 
  autolayer(final_table,Argentina)+  labs(title = "ARIMA Model (Default Parameters)", x = "Date", y = "Argentina realGDP")

fit_AR1 |> report()
## Series: Argentina 
## Model: ARIMA(0,0,0) w/ mean 
## 
## Coefficients:
##       constant
##         2.4733
## s.e.    1.1030
## 
## sigma^2 estimated as 37.76:  log likelihood=-96.53
## AIC=197.06   AICc=197.5   BIC=199.86
fit_AR1 |> gg_tsresiduals()+  labs(title = "ARIMA Model (Default Parameters)", x = "Date", y = "Argentina realGDP")

fit_AR1 |> augment() |>
  features(.innov, ljung_box,lag = 2)
## # A tibble: 1 × 3
##   .model           lb_stat lb_pvalue
##   <chr>              <dbl>     <dbl>
## 1 ARIMA(Argentina)   0.608     0.738
#diff by 1
final_ARG_RealGDP<- final_ARG_RealGDP%>%
  mutate(ARG_diff = difference(Argentina,1))

fit_AR_diff<- final_ARG_RealGDP|>
  model (ARIMA(ARG_diff))

fc_AR_diff = fit_AR_diff |>
  forecast(h = 5)
fc_AR_diff |> autoplot() + 
  autolayer(final_ARG_RealGDP,Argentina)+  labs(title = "ARIMA Model with Differencing", x = "Date", y = "Argentina realGDP")

fit_AR_diff |> report()
## Series: ARG_diff 
## Model: ARIMA(0,0,1) 
## 
## Coefficients:
##           ma1
##       -0.9332
## s.e.   0.1710
## 
## sigma^2 estimated as 39.51:  log likelihood=-95.47
## AIC=194.95   AICc=195.39   BIC=197.75
fit_AR_diff |> gg_tsresiduals()+  labs(title = "ARIMA Model with Differencing", x = "Date", y = "Argentina realGDP")
## Warning: Removed 1 row containing missing values (`geom_line()`).
## Warning: Removed 1 rows containing missing values (`geom_point()`).
## Warning: Removed 1 rows containing non-finite values (`stat_bin()`).

fit_AR_diff |> augment() |>
  features(.innov, ljung_box,lag = 2)
## # A tibble: 1 × 3
##   .model          lb_stat lb_pvalue
##   <chr>             <dbl>     <dbl>
## 1 ARIMA(ARG_diff)   0.203     0.904
#with Log of Argentina
fit_AR_log<- final_table|>
  model (ARIMA(log(Argentina)))
## Warning in log(Argentina): NaNs produced
fc_AR_log = fit_AR_log |>
  forecast(h = 5)
fc_AR_log |> autoplot() + 
  autolayer(final_table,Argentina)+  labs(title = "ARIMA Model with Log Transformation", x = "Date", y = "Argentina realGDP")

fit_AR_log |> report()
## Series: Argentina 
## Model: ARIMA(1,0,0) w/ mean 
## Transformation: log(Argentina) 
## 
## Coefficients:
##          ar1  constant
##       0.5618    0.7838
## s.e.  0.1993    0.0780
## 
## sigma^2 estimated as 0.1107:  log likelihood=-10.96
## AIC=27.91   AICc=28.84   BIC=32.12
fit_AR_log |> gg_tsresiduals()+  labs(title = "ARIMA Model with Log Transformation", x = "Date", y = "Argentina realGDP")
## Warning: Removed 12 rows containing missing values (`geom_point()`).
## Warning: Removed 12 rows containing non-finite values (`stat_bin()`).

fit_AR_log |> augment() |>
  features(.innov, ljung_box,lag = 2)
## # A tibble: 1 × 3
##   .model                lb_stat lb_pvalue
##   <chr>                   <dbl>     <dbl>
## 1 ARIMA(log(Argentina))    2.19     0.334

Let’s explore other ARIMA models.

Although the other ARIMA model looks like it’s moving, the long-term forecast of 0 seemed to be in favor with an AIC score of 159.51 (0,0,0) instead of 161(1,0,0), 162.7(2,0,0) and162.16 (2,1,0).

fit_AR2<- final_table|>
  model (ARIMA(Argentina ~ pdq(1,0,0)))|>
  report(fit_AR2)
## Series: Argentina 
## Model: ARIMA(1,0,0) w/ mean 
## 
## Coefficients:
##          ar1  constant
##       0.1472    2.1870
## s.e.  0.1894    1.0917
## 
## sigma^2 estimated as 38.31:  log likelihood=-96.23
## AIC=198.46   AICc=199.38   BIC=202.66
fc_AR2 = fit_AR2 |>
  forecast(h = 5)
fc_AR2 |> autoplot() + 
  autolayer(final_table,Argentina)+  labs(title = "ARIMA Model (1,0,0)", x = "Date", y = "Argentina realGDP")

fit_AR3<- final_table|>
  model (ARIMA(log(Argentina) ~ pdq(2,0,0)))|>
  report(fit_AR3)
## Warning in log(Argentina): NaNs produced
## Series: Argentina 
## Model: ARIMA(2,0,0) w/ mean 
## Transformation: log(Argentina) 
## 
## Coefficients:
##           ar1     ar2  constant
##       -0.6555  0.0850    3.1073
## s.e.   0.3459  0.3122    0.1214
## 
## sigma^2 estimated as 0.09213:  log likelihood=-9.64
## AIC=27.28   AICc=28.88   BIC=32.88
fc_AR3 = fit_AR3 |>
  forecast(h = 5)
fc_AR3 |> autoplot() + 
  autolayer(final_table,Argentina)+  labs(title = "ARIMA Model (2,0,0) on log(Argentina realGDP)", x = "Date", y = "log(Argentina realGDP)")

fit_AR4<- final_table|>
  model (ARIMA(Argentina ~ pdq(2,1,0)))|>
  report(fit_AR4)
## Series: Argentina 
## Model: ARIMA(2,1,0) 
## 
## Coefficients:
##           ar1      ar2
##       -0.5495  -0.2679
## s.e.   0.1993   0.1974
## 
## sigma^2 estimated as 51.16:  log likelihood=-97.35
## AIC=200.69   AICc=201.65   BIC=204.8
fc_AR4 = fit_AR4 |>
  forecast(h = 5)
fc_AR4 |> autoplot() + 
  autolayer(final_table,Argentina)+  labs(title = "ARIMA Model (2,1,0)", x = "Date", y = "Argentina realGDP")

#for test-statistics
glance_AR1     <- fit_AR1 |> glance()
glance_AR_diff <- fit_AR_diff |> glance() 
glance_AR_log  <- fit_AR_log |> glance() 
glance_AR2     <- fit_AR2 |> glance()
glance_AR3     <- fit_AR3 |> glance() 
glance_AR4     <- fit_AR4 |> glance() 

glance_AR_df <- bind_rows(glance_AR1, glance_AR_diff, glance_AR_log, glance_AR2, glance_AR3, glance_AR4)
glance_AR_df
## # A tibble: 6 × 8
##   .model                        sigma2 log_lik   AIC  AICc   BIC ar_ro…¹ ma_ro…²
##   <chr>                          <dbl>   <dbl> <dbl> <dbl> <dbl> <list>  <list> 
## 1 ARIMA(Argentina)             37.8     -96.5  197.  198.  200.  <cpl>   <cpl>  
## 2 ARIMA(ARG_diff)              39.5     -95.5  195.  195.  198.  <cpl>   <cpl>  
## 3 ARIMA(log(Argentina))         0.111   -11.0   27.9  28.8  32.1 <cpl>   <cpl>  
## 4 ARIMA(Argentina ~ pdq(1, 0,… 38.3     -96.2  198.  199.  203.  <cpl>   <cpl>  
## 5 ARIMA(log(Argentina) ~ pdq(…  0.0921   -9.64  27.3  28.9  32.9 <cpl>   <cpl>  
## 6 ARIMA(Argentina ~ pdq(2, 1,… 51.2     -97.3  201.  202.  205.  <cpl>   <cpl>  
## # … with abbreviated variable names ¹​ar_roots, ²​ma_roots

Trend Model

Now, I tried Forecasting with regression. Since my data doesn’t have seasonality, but only a little trend, I use Time-series Linear model for trend on Argentina’s realGDP data.

We can see a trend gown downwards. This can be useful for determining forecast later.

#first regression
fit_reg1 <- final_table |>
  model(TSLM(Argentina~ trend() ))
        
#regression plot
fit_reg1 |>augment()|>
  autoplot(.fitted, color ="red")+ 
  autolayer(final_table, Argentina)

#forecast
fc_reg1= fit_reg1 |>
  forecast(h = 10)

#Forecast plot with trend
fc_reg1 |> autoplot() + 
  autolayer(final_table,Argentina)

fit_reg1 |> report()
## Series: Argentina 
## Model: TSLM 
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.096  -3.633   1.329   5.147  10.556 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)   4.9637     2.2790   2.178    0.038 *
## trend()      -0.1607     0.1284  -1.252    0.221  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.086 on 28 degrees of freedom
## Multiple R-squared: 0.05298, Adjusted R-squared: 0.01916
## F-statistic: 1.566 on 1 and 28 DF, p-value: 0.22107
#for test-statistics
summary_reg1<- fit_reg1|>glance()
summary_reg1
## # A tibble: 1 × 15
##   .model  r_squ…¹ adj_r…² sigma2 stati…³ p_value    df log_lik   AIC  AICc   BIC
##   <chr>     <dbl>   <dbl>  <dbl>   <dbl>   <dbl> <int>   <dbl> <dbl> <dbl> <dbl>
## 1 TSLM(A…  0.0530  0.0192   37.0    1.57   0.221     2   -95.7  112.  113.  116.
## # … with 4 more variables: CV <dbl>, deviance <dbl>, df.residual <int>,
## #   rank <int>, and abbreviated variable names ¹​r_squared, ²​adj_r_squared,
## #   ³​statistic

Scenario-based Model

Now, I’m doing forecasting with scenarios. The first one is if there is a +-5% changes in Brazil realGDP, what will the forecast be with 80% and 95% interval. With AIC(105.4902) AICc(106.4133), it looks pretty good.

# Fit the TSLM model for Argentina using Brazil realGDP as a predictor
fit_Scn_brazil<- final_table %>%
  model(TSLM(Argentina ~ Brazil_realGDP)) %>%
  report()
## Series: Argentina 
## Model: TSLM 
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.189  -3.701   1.369   3.540  10.928 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     -0.0835     1.3053  -0.064  0.94945   
## Brazil_realGDP   1.0880     0.3610   3.014  0.00542 **
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.434 on 28 degrees of freedom
## Multiple R-squared: 0.245,   Adjusted R-squared: 0.218
## F-statistic: 9.085 on 1 and 28 DF, p-value: 0.0054242
#Layering regression line
fit_Scn_brazil |> augment() |>
  autoplot(.innov, colour = 'red') +
  autolayer(final_table,Argentina)

#setting scenario
new_cons <- scenarios(
  "descrease 5% in  Brazil realGDP" = new_data(final_table, 5) |>
    mutate(Brazil_realGDP = -5),
  " increase 5% in  Brazil realGDP" = new_data(final_table, 5) |>
    mutate(Brazil_realGDP = 5),
  names_to = "Scenario"
)
#forecast
fc_Scn_brazil <- forecast(fit_Scn_brazil, new_cons)

final_table|> 
  autoplot(Argentina)+
  autolayer(fc_Scn_brazil)+
  labs(title ="Argentina's realGDP forecast based on +- 5% changes in Brazil's ")

#for test-statistics
summary_Scn_brazil <-fit_Scn_brazil |> glance()
summary_Scn_brazil
## # A tibble: 1 × 15
##   .model  r_squ…¹ adj_r…² sigma2 stati…³ p_value    df log_lik   AIC  AICc   BIC
##   <chr>     <dbl>   <dbl>  <dbl>   <dbl>   <dbl> <int>   <dbl> <dbl> <dbl> <dbl>
## 1 TSLM(A…   0.245   0.218   29.5    9.09 0.00542     2   -92.3  105.  106.  110.
## # … with 4 more variables: CV <dbl>, deviance <dbl>, df.residual <int>,
## #   rank <int>, and abbreviated variable names ¹​r_squared, ²​adj_r_squared,
## #   ³​statistic

The second one has 3 scenarios: 1. 5% increase 2. 5% decrease 3. +5% in Cattle and -5% in Soybean Productions. The forecast will be with 80% and 95% interval. With AIC(114.6131) AICc(116.2131), it looks pretty good.

# Fit the TSLM model for Argentina using Cattle and Soybean Production as a predictor
fit_scn_soyCattle <- final_table %>%
  model(TSLM(Argentina ~ Cattle+Soybean)) %>%
  report()
## Series: Argentina 
## Model: TSLM 
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.4908  -5.0135   0.6733   5.0951   8.3626 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)  
## (Intercept)  2.19364    1.22563   1.790   0.0847 .
## Cattle      -0.06123    0.19196  -0.319   0.7522  
## Soybean      0.04109    0.05742   0.716   0.4804  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 6.231 on 27 degrees of freedom
## Multiple R-squared: 0.04264, Adjusted R-squared: -0.02827
## F-statistic: 0.6013 on 2 and 27 DF, p-value: 0.55527
fit_scn_soyCattle |> augment() |>
  autoplot(.innov, colour = 'red') +
  autolayer(final_table,Argentina)

new_cons <- scenarios(
  "descrease 5% in  production" = new_data(final_table, 5) |>
    mutate(Cattle = -5, Soybean = -5),
  " increase 5% in  production" = new_data(final_table, 5) |>
    mutate(Cattle = 5, Soybean = 5),
    " increase 5% in  Cattle, decrease 5% in Soybean production" = new_data(final_table, 5) |>
    mutate(Cattle = 5, Soybean = -5),
  names_to = "Scenario"
)

fc_scn_soyCattle <- forecast(fit_scn_soyCattle, new_cons)
final_table|> 
  autoplot(Argentina)+
  autolayer(fc_scn_soyCattle)

#for test-statistics
summary_scn_soyCattle <-fit_Scn_brazil |> glance()
summary_scn_soyCattle
## # A tibble: 1 × 15
##   .model  r_squ…¹ adj_r…² sigma2 stati…³ p_value    df log_lik   AIC  AICc   BIC
##   <chr>     <dbl>   <dbl>  <dbl>   <dbl>   <dbl> <int>   <dbl> <dbl> <dbl> <dbl>
## 1 TSLM(A…   0.245   0.218   29.5    9.09 0.00542     2   -92.3  105.  106.  110.
## # … with 4 more variables: CV <dbl>, deviance <dbl>, df.residual <int>,
## #   rank <int>, and abbreviated variable names ¹​r_squared, ²​adj_r_squared,
## #   ³​statistic

Vector Auto-Regression(VAR) Model

For the last method, I used. Vector AutoRegresssion. I’m having Argentina realGDP as the predicting variables and there are three models: Negative Gross Debt, Soybean+Cattle Combination, and Brazil realGDP. As you can see below, all of them are white noises. And AICc and AIC scores are in the lower end in all models of this project.

#vector autoregression models
#only using AICC because my dataset is not big.
fit_var_Debt <- final_table |>
  model(    
    aicc = VAR(vars(Argentina, Gross_debt_negative))
  )

fit_var_SoyCattle <- final_table|>
  model(
    aicc = VAR(vars( Argentina, Soybean, Cattle ))
  )

fit_var_Brazil <- final_table|>
  model(
    aicc = VAR(vars( Argentina,Brazil_realGDP))
  )

#Predicting Argentina with negatived Gross Debt

fit_var_Debt|>
  augment()|> 
    ACF(.innov) |>
  autoplot()+labs(title ="Argentina realGDP and its Negative Gross Debt Vector Auto Regression forecast")

fit_var_Debt |> 
  select(aicc)|>
  forecast(h = 10) |>
  autoplot(final_table) +labs(title ="Argentina realGDP and its Negative Gross Debt Vector Auto Regression forecast")

#Predicting Argentina ReaL GDP with Soybean and Cattle Production

fit_var_SoyCattle|>
  augment()|>
      ACF(.innov) |>
  autoplot()+labs(title ="Argentina realGDP and combination Soybean and Cattle Production of Vector Auto Regression forecast")

fit_var_SoyCattle |> 
  select(aicc)|>
  forecast(h = 10) |>
  autoplot(final_table)+labs(title ="Argentina realGDP and combination Soybean and Cattle Production of Vector Auto Regression forecast")
## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

## Warning in FUN(X[[i]], ...): NaNs produced

#Predicting Argentina ReaL GDP with Brazil Real_GDP
fit_var_Brazil|>
  augment()|>
  ACF(.innov) |>
  autoplot()+labs(title ="Argentina realGDP and Brazil realGDP Vector Auto Regression forecast")

fit_var_Brazil |> 
  select(aicc)|>
  forecast(h = 10) |>
  autoplot(final_table)+labs(title ="Argentina realGDP and Brazil realGDP Vector Auto Regression forecast")

#for test-statistics
#renaming models
glance_var_debt     <- fit_var_Debt |> glance()       |>mutate(.model = "VAR(vars(Argentina, Gross_debt_negative)")
glance_var_SoyCattle <- fit_var_SoyCattle |> glance() |>mutate(.model = "VAR(vars( Argentina, Soybean, Cattle ) ")
glance_var_Brazil <- fit_var_Brazil |> glance()       |>mutate(.model = " VAR(vars( Argentina,Brazil_realGDP)")


glance_var_df <- bind_rows(glance_var_debt, glance_var_SoyCattle, glance_var_Brazil)

Conclusion

#all models in the project
glance_var_df <- glance_var_df%>% select(.model, AIC, AICc, BIC)
glance_AR_df <- glance_AR_df%>% select(.model,AIC, AICc, BIC)
summary_scn_soyCattle <- summary_scn_soyCattle%>% select(.model,AIC, AICc, BIC)
summary_Scn_brazil <- summary_Scn_brazil %>% select(.model,AIC, AICc, BIC)
summary_reg1 <- summary_reg1%>%select(.model,AIC, AICc, BIC)

model_df <- bind_rows(glance_AR_df, summary_scn_soyCattle, summary_Scn_brazil, summary_reg1, glance_var_df)


model_df%>%arrange(desc(AIC))
## # A tibble: 12 × 4
##    .model                                       AIC   AICc   BIC
##    <chr>                                      <dbl>  <dbl> <dbl>
##  1 "VAR(vars( Argentina, Soybean, Cattle ) "  661.    41.2 701. 
##  2 "VAR(vars(Argentina, Gross_debt_negative)" 444.  -258.  475. 
##  3 " VAR(vars( Argentina,Brazil_realGDP)"     305.  -397.  336. 
##  4 "ARIMA(Argentina ~ pdq(2, 1, 0))"          201.   202.  205. 
##  5 "ARIMA(Argentina ~ pdq(1, 0, 0))"          198.   199.  203. 
##  6 "ARIMA(Argentina)"                         197.   198.  200. 
##  7 "ARIMA(ARG_diff)"                          195.   195.  198. 
##  8 "TSLM(Argentina ~ trend())"                112.   113.  116. 
##  9 "TSLM(Argentina ~ Brazil_realGDP)"         105.   106.  110. 
## 10 "TSLM(Argentina ~ Brazil_realGDP)"         105.   106.  110. 
## 11 "ARIMA(log(Argentina))"                     27.9   28.8  32.1
## 12 "ARIMA(log(Argentina) ~ pdq(2, 0, 0))"      27.3   28.9  32.9

Although log models shows a lot of potentials, my data have negative numbers, so this is not a good model.

However, The best model is TSLM(Argentina ~ Brazil_realGDP) with AIC of 105.49017. This is understandable as I’m playing safe percentage change, and the model’s line also layer most part of the original. Here’s the plot:

fit_Scn_brazil |> augment() |>
  autoplot(.innov, colour = 'red') +
  autolayer(final_table,Argentina)

final_table|> 
  autoplot(Argentina)+
  autolayer(fc_Scn_brazil)+
  labs(title ="Argentina's realGDP forecast based on +- 5% changes in Brazil's ")

The order of the best model for the forecasting of this data are clear: 1. TSLM/Scenarios based models 2. ARIMA models 3. Vector Auto Regression Models.

Data Sources: Real GDP data source: https://www.imf.org/external/datamapper/NGDP_RPCH@WEO/KOR/ARG/BRA

Real GDP for both Argentina, Brazil and South Korea extracted from IMF website.

Inflation data source: Inflation data is from Worlddata.info. Argentina: https://www.worlddata.info/asia/south-korea/inflation-rates.php South Korea:https://www.worlddata.info/america/argentina/inflation-rates.php Brazil:https://www.imf.org/external/datamapper/PCPIPCH@WEO/BRA?zoom=BRA&highlight=BRA Production Goods Data Source: https://www.fao.org/faostat/en/#data/QCL